The use of fractal geometry for the thermodynamic description of the three-dimensional elements of the crystal structure

Received: 25 April 2012; Revised: 28 June 2012; Accepted: 01 July 2012
This paper is written in Russian
Citation: V.B. Fedoseev. The use of fractal geometry for the thermodynamic description of the three-dimensional elements of the crystal structure. Lett. Mater., 2012, 2(2) 78-83


In this paper are described the thermodynamic regularities of distribution of the dispersed particles of the size of a given geometric shape. An ensemble of grains of the polycrystal is considered as a disperse system. We describe the equilibrium distribution of grain size and grain shape. It's argued that the fractal dimension and multifractality of polydisperse systems are determined by thermodynamic conditions and material properties and can be regarded as a thermodynamic charac-teristic, of dispersed system. It is shown that with the increasing temperature of crystalline material, the average fractal dimension of the three-dimensional elements of the structure is reduced.

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